Three-Stage Procedures for Selecting the Largest Normal Mean

SYNOPTIC ABSTRACT

We select, from k(≥2) independent normal populations, the one with the largest mean, where the common variance is unknown. Under the “indifference zone” approach of Bechhofer (1954), we consider three–stage selection procedures. Asymptotic second order expansions for the average sample size and the probability of correct selection are provided here for arbitrary k. The second order expansions show that our three–stage procedure enjoys the second–order asymptotic efficiency property, and gives us the asymptotic number of extra samples necessary over the sequential procedure of Robbins, Sobel and Starr (1968), and over the fixed sample approach, had the variance been known, of Bechhofer (1954). Computer simulations are used to explore moderate sample size performance.

Key Words and Phrases:

• Indifference zone
• average sample size
• probability of correct selection
• least favorable configuration
• asymptotic expansions